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PARAMETER DEPENDENCE OF SMOOTH STABLE MANIFOLDS
Barreira, Luis,Valls, Claudia Korean Mathematical Society 2019 대한수학회지 Vol.56 No.3
We establish the existence of $C^1$ stable invariant manifolds for differential equations $u^{\prime}=A(t)u+f(t,u,{\lambda})$ obtained from sufficiently small $C^1$ perturbations of a nonuniform exponential dichotomy. Since any linear equation with nonzero Lyapunov exponents has a nonuniform exponential dichotomy, this is a very general assumption. We also establish the $C^1$ dependence of the stable manifolds on the parameter ${\lambda}$. We emphasize that our results are optimal, in the sense that the invariant manifolds are as regular as the vector field. We use the fiber contraction principle to establish the smoothness of the invariant manifolds. In addition, we can also consider linear perturbations, and thus our results can be readily applied to the robustness problem of nonuniform exponential dichotomies.
CHARACTERIZATION OF TEMPERED EXPONENTIAL DICHOTOMIES
Barreira, Luis,Rijo, Joao,Valls, Claudia Korean Mathematical Society 2020 대한수학회지 Vol.57 No.1
For a nonautonomous dynamics defined by a sequence of bounded linear operators on a Banach space, we give a characterization of the existence of an exponential dichotomy with respect to a sequence of norms in terms of the invertibility of a certain linear operator between general admissible spaces. This notion of an exponential dichotomy contains as very special cases the notions of uniform, nonuniform and tempered exponential dichotomies. As applications, we detail the consequences of our results for the class of tempered exponential dichotomies, which are ubiquitous in the context of ergodic theory, and we show that the notion of an exponential dichotomy under sufficiently small parameterized perturbations persists and that their stable and unstable spaces are as regular as the perturbation.
Parameter dependence of smooth stable manifolds
Luis Barreira,Claudia Valls 대한수학회 2019 대한수학회지 Vol.56 No.3
We establish the existence of $C^1$ stable invariant manifolds for differential equations $u'=A(t)u+f(t,u,\lambda)$ obtained from sufficiently small $C^1$ perturbations of a \emph{nonuniform} exponential dichotomy. Since any linear equation with nonzero Lyapunov exponents has a nonuniform exponential dichotomy, this is a very general assumption. We also establish the $C^1$ dependence of the stable manifolds on the parameter $\lambda$. We emphasize that our results are optimal, in the sense that the invariant manifolds are as regular as the vector field. We use the fiber contraction principle to establish the smoothness of the invariant manifolds. In addition, we can also consider linear perturbations, and thus our results can be readily applied to the robustness problem of nonuniform exponential dichotomies.
Characterization of tempered exponential dichotomies
Luis Barreira,Joao Rijo,Claudia Valls 대한수학회 2020 대한수학회지 Vol.57 No.1
For a nonautonomous dynamics defined by a sequence of bounded linear operators on a Banach space, we give a characterization of the existence of an exponential dichotomy with respect to a sequence of norms in terms of the invertibility of a certain linear operator between general admissible spaces. This notion of an exponential dichotomy contains as very special cases the notions of uniform, nonuniform and tempered exponential dichotomies. As applications, we detail the consequences of our results for the class of tempered exponential dichotomies, which are ubiquitous in the context of ergodic theory, and we show that the notion of an exponential dichotomy under sufficiently small parameterized perturbations persists and that their stable and unstable spaces are as regular as the perturbation.
Ana Paula Barreira,Luís Catela Nunes,Maria Helena Guimarães,Thomas Panagopoulos 서울시립대학교 도시과학연구원 2019 도시과학국제저널 Vol.23 No.1
Creating liveable cities is a policy priority, especially for cities that are experiencing population loss. A decline in the number of inhabitants is commonly associated with low levels of residential satisfaction. However, such a supposition does not often find empirical support in shrinking cities. In the present study, we identify variables that influence the level of residential satisfaction, as well as those influencing residential attraction (captured by the intention of current residents to leave their city in the near future). The study is based on a face-to-face questionnaire administered to 701 residents in four shrinking Portuguese cities. As expected, lower levels of residential satisfaction lead to an increased intention to leave the city. The results also show that the variables explaining residential satisfaction mostly differ from those explaining residential attractiveness. The specific characteristics of each city influence citizens’ assessment of residential satisfaction, but the variables impacting residential attractiveness are universal.
Matiello, M.,Kim, H. J.,Kim, W.,Brum, D. G.,Barreira, A. A.,Kingsbury, D. J.,Plant, G. T.,Adoni, T.,Weinshenker, B. G. Ovid Technologies (Wolters Kluwer) - American Acad 2010 Clinical Neurophysiology Vol.75 No.4
<P>BACKGROUND: Detection of aquaporin-4-specific immunoglobulin G (IgG) has expanded the spectrum of neuromyelitis optica (NMO). Rare reports of familial aggregation have suggested a component of genetic susceptibility but these reports mostly antedated the discovery of the NMO-IgG biomarker and recently updated diagnostic criteria. METHODS: We report a case series describing the demographic, clinical, neuroimaging, and NMO-IgG serologic status of 12 multiplex NMO pedigrees with a total of 25 affected individuals. RESULTS: Twenty-one patients (84%) were women. Families were Asian (n = 5), Latino (n = 4), white (n = 1), or African (n = 2). Apparent transmission was either maternal (n = 5) or paternal (n = 2). In 1 family, 3 individuals had NMO; in the others, 2 individuals were affected. Sibling pairs (n = 6), parent-child (n = 4), and aunt-niece (n = 3) pairs were observed. Nineteen patients (76%) were NMO-IgG positive. Twelve (48%) had clinical or serologic evidence of another autoimmune disease. Familial occurrence of NMO occurs in approximately 3% of patients with well-established diagnosis of NMO. CONCLUSIONS: A small proportion of patients with NMO have relatives with this condition, but familial occurrence is more common than would be expected from its frequency in the general population. Familial NMO is indistinguishable from sporadic NMO based on clinical symptoms, age at onset, sex distribution, and frequency of NMO-IgG detection. One or 2 generations were affected and affected individuals represented a small fraction of family members. Taken together, these data suggest complex genetic susceptibility in NMO.</P>
Cosmic-ray positron fraction measurement from 1 to 30 GeV with AMS-01
AMS-01 Collaboration,Aguilar, M.,Alcaraz, J.,Allaby, J.,Alpat, B.,Ambrosi, G.,Anderhub, H.,Ao, L.,Arefiev, A.,Azzarello, P.,Baldini, L.,Basile, M.,Barancourt, D.,Barao, F.,Barbier, G.,Barreira, G.,Bat North-Holland Pub. Co 2007 Physics letters: B Vol.646 No.4
A measurement of the cosmic ray positron fraction e<SUP>+</SUP>/(e<SUP>+</SUP>+e<SUP>-</SUP>) in the energy range of 1-30 GeV is presented. The measurement is based on data taken by the AMS-01 experiment during its 10 day Space Shuttle flight in June 1998. A proton background suppression on the order of 10<SUP>6</SUP> is reached by identifying converted bremsstrahlung photons emitted from positrons.
RELATIVE COMPOSITION AND ENERGY SPECTRA OF LIGHT NUCLEI IN COSMIC RAYS: RESULTS FROM AMS-01
Aguilar, M.,Alcaraz, J.,Allaby, J.,Alpat, B.,Ambrosi, G.,Anderhub, H.,Ao, L.,Arefiev, A.,Arruda, L.,Azzarello, P.,Basile, M.,Barao, F.,Barreira, G.,Bartoloni, A.,Battiston, R.,Becker, R.,Becker, U.,Be IOP Publishing 2010 The Astrophysical journal Vol.724 No.1
ISOTOPIC COMPOSITION OF LIGHT NUCLEI IN COSMIC RAYS: RESULTS FROM AMS-01
Aguilar, M.,Alcaraz, J.,Allaby, J.,Alpat, B.,Ambrosi, G.,Anderhub, H.,Ao, L.,Arefiev, A.,Arruda, L.,Azzarello, P.,Basile, M.,Barao, F.,Barreira, G.,Bartoloni, A.,Battiston, R.,Becker, R.,Becker, U.,Be IOP Publishing 2011 The Astrophysical journal Vol.736 No.2
<P>The variety of isotopes in cosmic rays allows us to study different aspects of the processes that cosmic rays undergo between the time they are produced and the time of their arrival in the heliosphere. In this paper, we present measurements of the isotopic ratios H-2/He-4, He-3/He-4, Li-6/Li-7, Be-7/(Be-9+Be-10), and B-10/B-11 in the range 0.2-1.4 GeV of kinetic energy per nucleon. The measurements are based on the data collected by the Alpha Magnetic Spectrometer, AMS-01, during the STS-91 flight in 1998 June.</P>